String length

I am actually quite sure I have it right but my book would then be wrong so I have posted my problem here to see if I didn't do a embarassing mistake in arithmetics.1. The problem statement, all variables and given/known data
"Show that the energy equivalent of the length 10-18cm of a large extra dimension is roughly 20TeV"
-Zwiebach 2004
2. Relevant equations
ħ=c=1
ħc≈200MeVx10-15m
ls=√α
mc2=ħc/ l3. The attempt at a solution
Just some simple reforming first: